Proceedings of the 6th WSEAS International Conference on Simulation, Modelling and Optimization, Lisbon, Portugal, September 22-24,

Transcription

1 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, Larg dformation modling in soil-tillag tool intraction using advancd 3D nonlinar finit lmnt approach R. Jafari, T. Tavakoli Hashjin,S. Mina, M.H. Raoufat Th authors ar Ramin Jafari, Ph.D. Studnt, Dpartmnt of Agricultural Machinry, Collg of Agricultur, Tarbiat Modars Univrsity, Thran, Iran, and Tymour Tavakoli Hashjin, Associatd Profssor, Dpartmnt of Agricultural Machinry, Collg of Agricultur, Tarbiat Modarrs Univrsity, Thran, Iran, Sad Mina, Assistant Profssor, Dpartmnt of Agricultural Machinry, Collg of Agricultur, Tarbiat Modarrs Univrsity, Thran, Iran, Mohammad Hosin Raoufat, Associatd Profssor, Dpartmnt of Agricultural Machinry, Collg of Agricultur, Shiraz Univrsity, Iran, Corrsponding author: Ramin Jafari, Dpartmnt of Agricultural Machinry, Collg of Agricultur, Tarbiat Modars Univrsity, Thran, Iran; phon: ; fax: ; Abstract: - This papr aims to introduc a finit lmnt modl to invstigat th prformanc of bnt lg (BL) plow and invstigat th prformanc of nw dsign as compard to a convntional on using finit lmnt mthod approach (FEM).Th diffrnc btwn th modifid and convntional BL plows is th dirction of angl btwn th projction of cutting blad on horizontal plan normal to plow shank and th lin prpndicular to th plow shank in th sam plan. Th ffcts of BL plow gomtry on plow prformanc for both plows wr studid and th rsults wr vrifid xprimntally. Convntional (B1), and modifid (B2) dsigns of BL plow wr modld at thr rak angls (R1= 7.5, R2= 15 and R3= 22.5 ), thrfor a total six tratmnts wr considrd for both thortical and xprimntal studis. A thr dimnsional non linar finit lmnt modl was dvlopd using appropriat FEM softwar (ANSYS 8.1). Th soil mdia was considrd as lastic-prfctly plastic with Druckr- Pragr matrial modl. Soil mshing, contact lmnts and soil frictional proprtis wr updatd aftr ach incrmntal tim stp. Variation of draft forc as calculatd by th FEM modl indicats that th minimum and maximum draft forcs corrspond to B2R2 and B1R3 tratmnts rspctivly. Th xprimntal rsults of draft forc wr in good agrmnt with prdictd data. Ky-Words: - finit lmnt mthod; larg dformation; Modifid bnt lg plow; soil forcs 1. Introduction Svral rsarchrs hav dvlopd FEM modls of soil cutting by simpl tillag tools, subsoilrs and disk plows (Yong and Hanna, 1977; Kushwaha, 1995; Filk, 1999; Mouazn and Nmnyi, 1999; Abo-Elnor t al., 2004; Abu hamd and Rdr, 2003). Howvr availabl litraturs on 3D FEM analysis of soil tillag by unsymmtrical tillag tools ar scarc. Th unsymmtrical shap of BL plow and a narrow thicknss of its blad rquirs that th analysis to b nonlinar in both gomtrical and matrial aspcts. Furthrmor larg dformation imposs gomtrical nonlinarity in th prsnt analysis. Gomtrical nonlinarity happns whn a nod corrsponding to an lmnt in FE analysis movs largr than its lmntal siz. Also nonlinar soil matrial modl and th natur of contact lmnt incras th dgr of nonlinarity of analysis. It is not worthy that during soil failur by tillag tool; cracks propagation as wll as soil sparation is gnratd at diffrnt locations throughout th ntir soil body. But as th FEM tnds to discrt th matrial domain into finit numbr of lmnts (connctd by finit numbr of nods maintaining th continuity at all tims throughout th analysis). Th modling of cracks in FE analysis is practically impossibl. Thrfor positions whr soil failur may occur ar locatd by rcognizing th shar distribution fild. A high shar strss gnratd at any givn point indicats th locations whr th soil failur happns as cracks sparations. This will b followd in this study at th 1

2 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, dtrmination of soil failur positions in ordr to ovrcom th disadvantag of th FEM in doing so. This papr aims to: 1. Dvlop a modifid modl of BL plow to consum low draft forc and incras soil disturbanc fficincy. 2. Modl th tillag procss by BL plow in convntional and modifid dsigns using FEM approach. 3. Compar draft and vrtical forcs of BL plow calculatd by FEM and masurd xprimntally. 4. To invstigat th ffct of dsign paramtrs of BL plow on th variation of tnsil, comprssiv and shar strss in soil. 2. Matrials and Mthods 2.1. Blad gomtry Th diffrnc btwn convntional and modifid bnt lg plows is th angl btwn th projction of cutting blad on horizontal plan and th lin normal to th plow shank. This angl in convntional modl is inclind toward th front of th shank whr for modifid plow this angl is inclind toward rar of th shank. Th dimnsion of shank and blad assmbly is sn in fig.1. Fig.1. Dimnsions in millimtrs of th BL plow assmbly dvlopd in this study. Rak angl is dfind as an angl btwn shank- blad intrfacs with horizontal lin paralll to travl dirction. A total of four diffrnt rak angls could b obtaind by rotating th 2 plow about th horizontal axis (z-axis) using th hols on plow shank. In ordr to achiv a dpr pntration and rduc th soil rsistanc, th cutting dg of both plows wr sharpnd to 45. Prliminary soil-bin xprimnts by authors indicat that th modifid BL plow tills bttr than convntional on spcially at rak angl of 15 (Jafari t al, 2005) Finit lmnt formulation Th Elastic-Plastic modl dscribs an lastic, prfctly plastic rlationship. Strsss ar dirctly proportional to strain until th yild point is rachd. Byond th yild point, th strss-strain curv is prfctly horizontal. A function which dscribs th locus of th yild point is calld th yild function. Th yild function of th Druckr- Pragr lastic prfctly plastic matrial modl (F) can b xprssd as follows (Ansys documntation): F = 3 βσ T m + [ { S} [ M ]{ S}] 2 Whr: σ = th man or hydrostatic strss= m 1 ( σ + σ + σ ) x y z 3 {S}= th dviatoric strss quation β = matrial constant and is qual to β = 2Sinϕ 3(3 Sinϕ) Th matrial yild paramtr is dfind as σ y = 6cCosϕ 3(3 Sinϕ) Whr: C and ϕ ar th input soil cohsion valu and angl of soil intrnal friction, rspctivly. Soil plasticity is formulatd using th thory of incrmntal plasticity (Hill,

3 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, ). Onc a matrial bgins to yild, th incrmntal strain can b dividd into lastic and plastic componnts. p { dε } = { dε } + { dε } Only lastic strain incrmnts dε will caus strss changs. As a rsult, strss incrmnts can b writtn as follows: p { dσ} = [ C ]{ dε } = [ C ]({ dε} { dε }) A yild function, F, is a function of normal and shar strss, so an incrmntal chang in th yild function is givn by: df= dσ x + dσ y + dσ z + dτ xy = { }{ dσ} τ x y Th thory of incrmntal plasticity dictats df will b qual to zro whn th strss stat is on th yild surfac. This condition is trmd th natural loading condition, and can b writtn mathmatically as: df = { }{ σ} = 0 d Th plastic strain is postulatd to b: { G ε } = λ{ } d p Whr, G and λ ar plastic potntial function and plastic scaling factors, rspctivly. Finally th incrmntal strss corrsponding to a givn incrmntal strain is obtaind as follows: { dσ} = ([ C ] [ C ]){ dε} 2.3. Finit lmnt msh and boundry conditions Th soil mdia is modld as Cm, (lngth width hight) cub of solid matrial. At th placs that BL contacts with soil, th shap of BL plow is carvd into th soil. For both soil and blad, lmnt solid 45 is usd. Solid 45 is a brick lmnt with 8 nods and 3 dgrs of frdom at ach nod (U x, U y, U z ). This lmnt coms in svral shaps (Ttrahdral, Hxahdral ). For BL and th soil in th vicinity of BL, mappd hxahdral brick lmnts ar usd. In othr p z xy 3 parts of th soil in which this shap of lmnt couldn t b usd, fr ttrahdral lmnts ar placd. Sinc th thicknss of BL plow is only 1 Cm, th siz of lmnts of BL could b utmost 1 Cm and th siz of soil lmnts in contact with plow should b th sam. Mor than lmnts ar usd in this modl. Most of th analysis was carrid out through 30 mm of blad displacmnt in th horizontal plan along th x axis dirction. For a typical 3D modl, a solution tim of about 10 hours was ndd to account for whol 30 mm displacmnt using P5 computr with 1024 MB mmory. Anothr rason for choosing 30 mm blad displacmnt is th blad forcs hav rachd a stady stat during this tim priod as mntiond by Abo-Elnor, tal, Vry dns msh is usd to obtain a highly accurat quantitativ analysis. Each fac of soil mdia is constraind so it couldn t mov normal to th fac. Th nods on blad- soil intrfac hav a spcific displacmnt along blad surfac. Also th intrnal nods ar fr in thr dirctions. Th boundary conditions considrd on th BL plow is so that prvnts all of its displacmnt and rotation unlss in th dirction of tool travl. In this dirction a controlld displacmnt is imposd on a pilot point. A pilot point is a point that is joind to som parts of BL and all movmnt and forcs of this point automatically transfr to whol body of BL plow. To modl th contact surfacs btwn BL plow and soil mdia, flxibl surfac to surfac contact lmnts ar usd. This kind of contact lts th soil slip on th BL surfac and also transfr th loads (forcs and displacmnts) btwn soil and tillag tool. It also lts th soil sparat from blad. All ths procsss ar controlld by paramtrs lik Normal and tangntial stiffnss. Ths paramtrs control th sparation and slippag of soil rlativ to blad, rspctivly. Furthrmor, ths two paramtrs play an important rol in convrgnc of analysis. Strngth bhavior of contact is controlld by contact cohsion and friction cofficint and maximum shar strss. Tangntial stiffnss is masurd by

4 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, dirct shar box and coulomb s friction laws. To mak a targt lmnt it is ncssary to put a targt lmnt on targt surfac and a contact lmnt on contact surfac as a rsult th contact lmnt will b automatically producd btwn ths two suprficial lmnts. Targ170 and Cont174 lmnts ar usd to produc contact. FE analysis is fundd on a small displacmnt maning that on can impos a displacmnt up to 15% of lmnt siz to an lmnt. Som programs lik ANSYS upgrad th gomtry of lmnt during th analysis. Thrfor it is possibl to hav a bit mor displacmnt. Although thr ar a numbr of lmnts that work togthr and whnvr on of thm yilds, othrs tolrat th rmindr of forc, yt thos plastic lmnts couldn t tolrat xcssiv displacmnt and caus th analysis to divrg. FE analysis was carrid out in six diffrnt tratmnts (3 rak angl 2blad gomtry). Convntional (B1), and modifid (B2) dsigns of BL plow wr modld at thr rak angls (R 1 = 7.5, R 2 = 15 and R 3 = 22.5 ). All analyss wr don in 10 incrmntal tim stps (ach stp 3 mm) and th strsss and forcs wr rcordd at th nd of ach tim stp. Th working dpth for FE modl and xprimntal tst was 250 mm. 3. Rsults and discussion BL plow draft, vrtical and latral forcs wr calculatd from th summation of th ractions of th contact lmnts that act on pilot point. Also masurd and prdictd raction forcs data wr compard. Th soil strss and strain wr compard for both dsigns Draft forc Prdictd Draft forc (N) this procss is that th plastic strain in ach lmnt occurs in vry low displacmnt. In th nxt stp of tool motion, th soil plastic yildd lmnts transfr forcs to th nxt lmnt and its forc tnds to bcom constant. Th graph of th variation of draft forc against blad displacmnt shows that th draft forc of convntional BL plow is mor than modifid on so that th B 1 R 3 tratmnt consums maximum draft forc. Th rat of incrasing draft forc with incrasing rak angl was not noticd in modifid BL plow so that th B 2 R 2 tratmnt consumd minimum draft Draft forc (N ) Displacmnt (mm) Fig.2. FEM calculatd draft forc of BL plow as a function of displacmnt Rak angl (dgrs) Convntional blad ( Prdictd) Convntional blad ( Masurd) Modifd blad (Prdictd) Modifid blad (Masurd) Fig.3. Masurd and prdictd draft forcs of BL plow vrsus rak angl. B1R1 B1R2 B1R3 B2R1 B2R2 B2R3 Fig. 2 shows th FEM calculatd componnt of draft forc against displacmnt for th six tratmnts studid. Th rat of incras of draft forc is rlativly high at low displacmnt, and dcrass as displacmnt incras. Th rason for 4 In th soil bin tst th maximum draft forc was sn aftr longr displacmnt than that prdictd by FEM. Th xtnsion of loos horizon might intrprt such divrgnc, bcaus th soil within this loos horizon might hav

5 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, bn comprssd for longr displacmnt bfor it collapsd. On th othr hand, for th FEM modl th homognous compactd body collapsd aftr shortr BL plow displacmnt. Hnc it can b concludd that maximum draft forc hav bn occurrd arlir. Th comparison of th masurd and prdictd draft forc of convntional BL plow as a function of rak angl shows that any incras in rak angl rsults in an incras in tool draft forc (fig.3). Th prdictd BL plow horizontal raction forc from th FEM modl xcdd th masurd ons for both plow dsigns. Th ovr prdiction rror of draft forc can b attributd to soil failur mchanism. Crack formations and fragmntation of th soil during th soil bin tst wr not proprly accountd for in th FEM modl, whr th Druckr-Pragr lastic-prfctly plastic modl with th gnral flow rul of associatd plasticity was adoptd. Th amount of draft ovr prdiction rangd from 9.9 to 18.3%. Changing th dirction of angl btwn projction of cutting blad on horizontal plan and th lin normal to th shank causs th surfac of th soil to b th first point to com in contact with cutting dg. This backward rotation causs th soil cutting procsss start from surfac and propagat to th sub soil, as a rsult th surcharg prssur which applis to th blad is mrly th wight of loos soil. Thrfor rduction in th amount of surcharg prssur acting on th blad is considrd as th most important caus of draft forc rduction in th modifid modl, furthrmor tnsil cracks appars instad of comprssiv ons in modifid BL plow, which allviat th draft forc. Also th sam rsults wr sn for vrtical forc Soil displacmnt Th distribution of th vrtical and forward soil displacmnt filds calculatd from th FEM modl aftr 20 mm blad displacmnt. In th zon citd in front of th BL plow shank and abov th cutting blad, th soil movs upward, forward and sidways with rspct to th original position. Such arbitrary motions indicat that shar distortion occurrd throughout th zon. Figs.4 shows upward soil displacmnts distribution contour du to typical BL plows. Maximum upward soil displacmnt usually occurs within a littl distanc in front of th plow shank, and maks a wdg shap soil uphaval. Th soil slop in th small gap from th maximum surfac uphaval point down to th front dg of th shank can b intrprtd by th rsistanc action of th intrfac friction against th upward sliding of th shank adjacnt soil particls. Th maximum upward soil displacmnt shows th ability of plow to cut, loos and turn th soil. Th comparison of th amount of maximum upward soil displacmnt in front of th shank show that th modifid BL plow can mov th soil upward mor than convntional on (Tabl.1). Tabl.1. Comparison of maximum upward soil displacmnt in front of plow shank (displacmnts ar in millimtr). Rak angl Blad dsign B1(Convntional blad) B2(Modifid blad) R 1(7.5 o ) R 2(15 o ) R 3(22.5 o ) Man soil upward displacmnt

6 Procdings of th 6th WSEAS Intrnational Confrnc on Simulation, Modlling and Optimization, Lisbon, Portugal, Sptmbr 22-24, Th FEM rsults indicat that th maximum soil loosning and upward displacmnt is sn in modifid BL plow at rak angl of 15. Fig.4. Typical upward soil displacmnt distribution contour for convntional BL plow at 22.5 rak angl aftr 20mm blad displacmnt (displacmnts ar in mtr). Rfrncs [1] Abo-Elnor, M., Hamilton,R., Boyl. J.T., Simulation of soil-blad intraction for sandy soil using advancd 3D finit lmnt analysis. Soil and Tillag Rsarch. 75: [2] Abu-Hamdh, N.H., Rdr R.C., A nonlinar 3D finit lmnt analysis of th soil forcs acting on a disk plow. Soil and Tillag Rsarch. 74: [3] ANSYS documntation, Rlas 8.1., 2004 ANSYS Inc, Company. [4] Filk, J.M Finit lmnt modling of th intraction of th cutting dg of tillag implmnts with soil. J. agric.engng.rs. 74: [5] Jafari,R., Raoufat, M.H., Tavakoli Hashjin,T., Soil-Bin Prformanc of a Modifid Bntlg Plow. submittd in th journal of applid nginring in agricultur. [6] Kushwaha, R.L., Shn, J., Finit lmnt analysis of dynamic intraction btwn soil and tillag tool. Transactions of th ASAE, Vol. 37(5): [7] McKys, E., Soil Cutting and Tillag. Elsvir Scincs, Amstrdam, 292 pp. [8] Mouazn, A.M., Nmnyi, M., Finit lmnt analysis of subsoilr cutting in non-homognous sandy loam soil. Soil and Tillag Rsarch. 51: [9] Yong, R.N., Hanna, A.W., Finit lmnt analysis of plan soil cutting. J. Trramchanics, Vol. 14(3):